Simple Explanation of Zipf's Mystery via New Rank-Share Distribution, Derived from Combinatorics of the Ranking Process
32 Pages Posted: 21 Feb 2017
Date Written: February 15, 2017
This work provides a surprisingly simple explanation of Zipf’s law and derives an exact formula for Zipf’s distribution. It also presents a new rank-share distribution and illustrates that peculiar dependency between a share and 1/rank, observed in many publications, is descended from expected values of various ranks in the new distribution. All conclusions, formulas and charts presented here were tested against publicly available statistical data in different areas. The correlation between predicted and observed dependences are really impressive. For large datasets (> million records), the average correlation coefficients were (R=0.999, R2 = 0.997, Theil's U2 = 0.0135). Monte-Carlo simulations were performed as the additional evidence.
Keywords: Zipf, Explanation, Formula, Rank, Share, Distribution
JEL Classification: C40, C60, D30, D40, R11, R12, R15
Suggested Citation: Suggested Citation